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Assume A lied. Then the number does not have 2 digits. But it cannot have 1 digit, since then it could not be divisible by 25. Nor could it have more than 2 since the only suchnumber that is a divisor of 150 is 150 itself, and that's not it according to C. Thus it is impossible that A was the "lone liar".
So we move on and assume B lied. Then the number is not a divisor of 150. But the only three two digit numbers that are divisible by 25 are 25, 50 and 75, all of which are divisors of 150. So B isn't the culprit either.
If C was the liar, then the number is indeed 150, which can't happen because it must have two digits according to A.
Finally if D lied, the number is not divisible by 25. This is possible with all other statements still being true. (For example if the number is 10 or 30.)
Therefore we know it's D that is the liar here. (Unfortunately we still cannot determine the number exactly.) |
